Outline
Singular
Contributors
History
Algorithms
Libraries
Comparisons
Examples
Singular20
Availability

Kernel Functionality and Algorithms
 Standard basis (Groebner basis) algorithms
 Syzygies and free resolutions of modules:
 Standardbasis driven, Schreyer's, La Scala's, Hilbertdriven
algorithm
 Ext^{i}, Masseyproducts
 Ideal Theory:
 Intersection, ideal quotient, elimination, saturation,
primary decomposition, radical ideal
 Combinatorics:
 dimensions, Hilbert series, multiplicities,
etc
 Multivariate polynomial computations:
 gcd, resultant, factorization
 Characteristic sets:
 Wu's method
 Singularity Theory:
 Milnor, Tjurina numbers, Arnold's classification,
HamburgerNoether (Puiseux) development, T^{1}, T^{2},
deformations of isolated singularities, monodromy, moduli of
space curves
